Sphere Volume Examples

See how to use the formula with real-world examples.

Example 1: Find the volume (radius = 3 cm)

V = &frac43; × 3.1416 × 3³ = 113.10 cm³
Step-by-Step Solution:

1. Write down the sphere volume formula: V = 4/3 × π × r³

2. Substitute radius r = 3 cm into the formula: V = 4/3 × 3.14159 × 3³

3. Calculate 3 cubed: 3³ = 27

4. Multiply 4/3 × π × 27 = 113.10 cm³ (or exactly 36π cm³).

Example 2: Find the volume (diameter = 10 cm)

r = d/2 = 10/2 = 5 cm
V = &frac43; × 3.1416 × 5³ = 523.60 cm³
Step-by-Step Solution:

1. The diameter is given as 10 cm. Find the radius: r = d / 2 = 10 / 2 = 5 cm.

2. Apply the sphere formula: V = 4/3 × π × 5³.

3. Compute 5 cubed: 5³ = 125.

4. Multiply: 4/3 × 3.1416 × 125 ≈ 523.60 cm³ (approx 0.524 Liters).

Example 3: Find the radius (volume = 904.78 cm³)

r = √((3 × 904.78) / (4 × 3.1416)) = 6.00 cm
Step-by-Step Solution:

1. Rearrange the volume formula to solve for radius: r = ∛((3 × V) / (4 × π)).

2. Multiply volume by 3: 3 × 904.78 = 2714.34.

3. Divide by 4π (approx 12.5664): 2714.34 / 12.5664 ≈ 216.

4. Take the cube root: ∛216 = 6.00 cm. The diameter is 12.00 cm.

Related Pages: Sphere Volume Calculator | Sphere Surface Area | Sphere Formulas